Siberian Advances in Mathematics

, Volume 25, Issue 1, pp 56–75 | Cite as

Asymptotics of mean value points in the Schwarz theorem for divided differences



We establish inequalities describing the asymptotic behavior of mean value points in the sense of the Schwarz theoremfor general divided differences constructed for a function with a certain growth order at a given point. These inequalities generalize a number of known results, in particular, of ones connected with the asymptotics of Lagrange points in the Taylor formula.


divided difference Schwarz theorem mean value theorem B-spline Peano kernel asymptotics of mean value points 


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© Allerton Press, Inc. 2015

Authors and Affiliations

  1. 1.Southern Mathematical Institute of VSC RAS and the Government of the Republic of North Ossetia — AlaniaVladikavkazRussia

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